Graham was born in Torrance, California. Growing up in Denver, Colorado, he attended Thomas Jefferson High School. Graham won the Randy Brewer award, which was given to the school's most inspirational player. During his time there, he played the positions of tight end, outside linebacker, long snapper, and placekicker. As a senior, he caught 33 passes for 741 yards (22.45 yards per reception) and six touchdowns, and recorded twelve quarterback sacks and 29 total tackles in just seven games. He also lettered three times in basketball.
At Thomas Jefferson High school and later at the University of Colorado, Graham wore jersey No. 89, the number that former New York Giants tight end Mark Bavaro wore during his pro career. As a child Graham idolized Bavaro, who has since followed Graham's career and has come to befriend him in his adult life.
While attending the University of Colorado, Graham played for the Colorado Buffaloes football team from 1998 to 2001. Nicknamed Grahambo, he was a prolific receiver for the Buffaloes, where he also started two games playing fullback during his freshman season before switching to tight end. After his senior season in 2001, he won the John Mackey Award as the nation's best tight end, was a first-team All-Big 12 selection, and was recognized as a consensus first-team All-American. He finished his college career with 106 receptions for 1,543 yards and 11 touchdowns.
In the first round of the 2002 NFL Draft, the Patriots selected Graham with the 21st overall choice. Early in his career he was known for dropping too many passes and suffering apparent lapses of concentration. He improved greatly in this aspect of his playing and also made himself known as an excellent blocking tight end. In his rookie season, Graham recorded 15 receptions for 150 yards, and one touchdown. He added four tackles on special teams. In 2003, he started nine games and recorded 38 catches for 409 yards and four touchdowns. By 2004, Graham was fully integrated into the Patriots' system. He had 30 receptions for 364 yards and seven touchdowns. The Patriots won the Super Bowl at the end of each of these seasons. Graham was named a Patriots team captain on December 6, 2006.
Graham was signed by the Denver Broncos on March 6, 2007. The Broncos awarded Graham a five-year, $30 million contract. The deal included $15 million in guaranteed money that was distributed as a $10 million signing bonus along with a first-year roster bonus of $5 million.
He was voted offensive captain along with quarterback Jay Cutler for the 2008 season.
Daniel Graham was featured on the cover of the October 12, 2009 issue of Sports Illustrated magazine. The cover photo shows Graham cradling the football in his left arm and hurdling an unnamed Dallas Cowboys player during the October 4, 2009 contest where the Broncos defeated the Cowboys by the score of 17-10.
On March 2, 2011, the Broncos released Graham.